The goal of this research is the development of semi-parametric methodology for analyzing the effect of covariates on event time distributions that arise in Acquired Immune Deficiency Syndrome (AIDS) epidemiological studies and clinical trials. We propose to develop methods for analyzing data from studies where latency is ascertained retrospectively from among AIDS cases. Such truncated data are available from studies involving individuals with AIDS who were infected by contaminated blood transfusions, and from current studies involving children with AIDS, who were infected in utero. We will develop methods for applying the proportional hazards model and isotonic regression for estimation and testing for the effect of covariates on the truncated event time distribution, and apply these methods for analysis of the latency distribution in AIDS. We will develop methods for analyzing the event time distributions from (prospective or retrospective) screening studies, where the infection time is not known exactly, but rather only known to lie in an interval which is of different length for each individual. Such interval censored infection times result in interval censored latency times. In this case, it is not possible to analyze either the infection time or latency distributions without calculating the joint distribution. We propose to develop methods for analyzing the effect of covariates on a bivariate event time distribution from doubly interval censored data. We will develop non-parametric methods for estimating the time to failure from an AIDS clinical trial which takes into account the occurrence of another time-dependent auxiliary event such as disease progression. In addition, we will develop a test for comparison of two or more therapies which utilizes the information on the auxiliary event.